Degrees to Radians Calculator

About this calculator

The radian is the natural, dimensionless unit of angle used throughout mathematics: one radian is the angle subtended when the arc length along a circle equals its radius, and a full circle measures exactly 2π radians instead of 360 degrees. Converting is a straightforward ratio: radians = degrees × (π/180), so 90° becomes π/2, 180° becomes π, and 45° becomes π/4.

Nearly every trigonometric function in programming languages and calculus expects radians, not degrees — Math.sin() in JavaScript, sin() in Python’s math module, and the derivative rules for sine and cosine all assume radian input, which is why the conversion trips up so many students moving from geometry to calculus or code. Physicists and engineers also work natively in radians when dealing with angular velocity (rad/s) and angular acceleration, since the radian-based formulas for arc length and rotational motion come out cleanly without extra conversion factors.

Enter an angle in degrees and this calculator converts it to radians both as a decimal and as an exact multiple of π, so you can see the fraction as well as the numeric value.